Seminar on Banach and Metric Space Geometry

Date: February 15, 2019

Time: 11:00AM - 12:00PM

Location: BLOC 628

Speaker: Petros Valettas, University of Missouri

Title: Gaussian concentration and convexity

Abstract: We will discuss new forms of concentration and anti-concentration phenomena explained by convexity rather than isoperimetry. On the side of applications, this perspective allows for superconcentration and convexity to be melted together in order to obtain strong small ball and small deviation estimates in normed spaces. In this framework, the l_∞-structure arises naturally as the (approximate) extremal. The underlying principle dictating these phenomena is rooted in the sensitivity of the variance. Based on a joint work with G. Paouris and K. Tikhomirov.